Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/233346 
Year of Publication: 
2019
Series/Report no.: 
Discussion paper No. 131
Publisher: 
Aboa Centre for Economics (ACE), Turku
Abstract: 
We give a proof of the existence of a Nash equilibrium forn-personnormal form games when each player's utility function is continuousw.r.t. strategy profiles, and concave and differentiable w.r.t. his ownstrategy. The proof uses only elementary mathematical tools such asmathematical induction. We show that this equilibrium existence re-sult is sufficiently general to imply the Brouwer Fixed Point Theorem.The Kakutani Fixed Point Theorem is obtained as a corollary by usingstandard techniques.
Subjects: 
Nash equilibrium
fixed-point theorem
JEL: 
C72
Document Type: 
Working Paper

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